What is type 3 grammar? Explain its properties

Type 3 grammars are regular grammars that describe regular / formal languages.

These grammars contain production rules consisting of the following −

• Only one non-terminal at the left hand side,

• The right hand side has a single terminal and may or may not be followed by non terminals.

Example

A → ε , A → a, A → b, A → aA etc.

Types

There are two types of regular grammars namely −

• Right linear / Right regular grammar

• Left linear / Left regular grammar

Let us learn about these two types of grammar in detail.

Right linear grammar

This is a regular grammar with the production rules of the form

A → α (or) A → α B

Where, A, B → non terminal symbols α → terminal symbol

These grammars are right-branching in nature, since the substitution is done for the right most non terminal, if available.

Left linear grammar

This is a regular grammar with the production rules of the form −

A → α (or) A → B α

Where, A and B are non terminals and α is a terminal symbol.

Since the substitution is done for the leftmost non-terminal, these grammars are left branching in nature.

Properties of Regular grammars

The regular grammars generates regular languages which are closed under the following −

• Union

• Concatenation

• Intersection

• Complementation

• Difference

• Reversal

• Reversal

• Closure

• Homomorphism

• Inverse homomorphism.